Graham, who has floated a presidential run himself, was a supporter of the immigration reform bill that passed the Senate last year.

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"If we don't at least make a down payment on solving the problem and rationally dealing with the 11 million [people in the country illegally], if we become the party of self-deportation in 2015 and 2016, then the chance of winning the White House I think is almost nonexistent," Graham said on CNN's "State of the Union" in an interview posted Sunday.

Graham also called for a measure to help the "Dreamers," who are people brought to the U.S. illegally as children. President Obama took executive action in 2012 to grant such people legal status, and then expanded his actions after the midterm elections to include more people.

"If the Republican Party cannot muster the political courage to deal with the Dream Act children in a fair and balanced way after we secure our border, that says a lot about the Republican Party's future regarding the Hispanic community," Graham said. "I don't believe most Americans would fault the Republican Party if we allowed children who have been here since they're babies to assimilate into society with a pathway to citizenship after we secure our borders."

Asked if he would seek the presidency, Graham demurred, but did tout his credentials.

"I think over the last several years, I've been more right than wrong when it comes to foreign policy, and the next president of the United States has got a world on fire that they must deal with and re-establish ourselves as the hope for freedom," he said.

"I think i have a unique capability to do things like that, but at the end of the day, running for president is a monumental task," he added. "Whether or not there's a pathway forward for me, I don’t know. I'll look at it in 2015."

Despite his possible presidential hopes, Graham also offered praise for former Florida Gov. Jeb Bush, who supports immigration reform, and who opened up a lead on the GOP field with 23 percent support in a new CNN/ORC poll.

"Jeb Bush would be an excellent candidate," Graham said. "I think he could win in 2016, I believe he could carry Florida. He’s got rational, logical views on immigration; he was a very good governor."